Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60146 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | D4×#41×C17 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
2756 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,26,24,27,29,34,31)(25,28,33,30,32,35,37,36);(19,21);(22,24,26,29,27,31,34,23)(25,30,33,35,32,36,37,28);(22,25)(23,28)(24,30)(26,33)(27,32)(29,35)(31,36)(34,37);(25,32)(28,35)(30,36)(33,37)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53134);